A nonlinear optical material is one that gives a nonlinear optical response when exposed to intense radiation. When exposed to normal light, such optical properties as the refractive indices of materials change linearly with light intensity. But when the intensity is great enough, as with laser light, these properties can vary as the square, cube or higher power of an applied electromagnetic field; or as the product of two, three or more different fields applied at once.
This is because optical properties depend on the degree of charge separation (polarization) induced by light. Total polarization of a molecule or region of a substance by an applied electromagnetic field is the sum of all the intrinsic, first-order, second-order or higher-order polarizations: EQU P=P.sub.o +.alpha.E+.beta.EE+.gamma.EEE+. . .
where P is the total dipole moment, P.sub.o is the intrinsic dipole moment, and .alpha., .beta. and .gamma. are first-, second- and third-order hyperpolarizabilities.
Such changes in the overall polarization of a material by an applied field result from all of the individual contributions to the dipole moment of a molecule or region caused by the field: EQU P=P.sub.o +.sub..chi..sup.(1) E+.sub..chi..sup.2) EE+.sub.102.sup.(3) EEE+. . .
where P is the total polarization, P.sub.o is the intrinsic polarization, the .sub..chi. s are first-, second-, third- and higher-order susceptibility coefficients, and the Es are either different electromagnetic fields or photons of the same kind.
Nonlinear optical effects take their name from their origin as powers or products of electromagnetic fields. The effects themselves are interactions of photons of light with photons of the same frequency or photons of different frequencies to produce photons of combined frequency.
The various optical linear and nonlinear susceptibilities and hyperpolarizabilities are related to the corresponding nonlinear effects and to possible applications in Table I. The microscopic entity at the origin of the nonlinear behavior would be a molecule in the case of an organic molecular crystal.
TABLE I ______________________________________ Possible Order Crystal Molecule Effects Utilization ______________________________________ 1 .chi..sup.(1) .alpha. refraction optical fibres 2 .chi..sup.(2) .beta. generation frequency of second doublers harmonic .omega. + .omega. .fwdarw. 2.omega. frequency optical mixers mixing .omega..sub.1 .+-. .omega..sub.2 .fwdarw. .omega..sub.3 parametric optical para- amplification metric oscil- .omega..sub.3 .fwdarw. .omega..sub.1 + .omega..sub.2 lators pockets electro- effects optical modula- .omega. + E(O) .fwdarw. .omega. tors 3 .chi..sup.(3) .gamma. 4-wave mixing Raman coherent spectroscopy phase grat- real time ings holography Kerr effect ultra high- speed optical gates optical bi- amplifiers, stability amplitude choppers and logical gates ______________________________________
As shown in Table I, the simplest second-order nonlinear effect is frequency doubling. Laser light enters a substance and emerges as light of double the frequency (half the wavelength). Frequency doublers could convert infrared light into visible light for easier detection of signals.
Alternatively, pumping of a substance with laser light of one frequency could cause it to lase at two different frequencies. Because the values of the two new frequencies depend on the angle at which the original beam enters the solid, adjusting the angle opens the way to tunable lasers, whose new frequencies extend their range of use.
Instead of light, one of the fields can be electrical. At one electric field and angle of incidence, the incoming light can be guided along the substance, which becomes a wave guide, in one preferred direction. Changing the frequency or angle of incidence may cause the substance to stop being a wave guide. Such behavior may lead to optical on-off switches. Other nonlinear optical effects could produce light-signal modulation or amplification.
The intensity of nonlinear optical effects decreases as the order increases. Thus, third-order effects are weaker than second-order ones. At the present time, effects of orders higher than three are too weak to be of interest for practical devices, though physicists may use them in theoretical studies. Third-order effects are useful because they are not highly dependent on ordering of molecules or regions in substances. Second-order effects are stronger, but molecules or regions must be acentric and are usually highly ordered.
Currently, the only technologically useful nonlinear optical materials are certain inorganic crystals, such as LiNbO.sub.3. However, the potential of organic materials to exhibit nonlinear optical properties has been extensively investigated in recent years, and a number of polymeric and nonpolymeric organic compounds which exhibit substantial optical nonlinearities have been identified. See, D. J. Williams, Angew. Chem. Int. Ed. Engl., 23, 690 (1984).
Second-order effects in organic or inorganic molecules result from enhancement of polarization in one direction and inhibition in another. For example, p-nitroaniline has a large molecular hyperpolarizability, .beta., due to the natural tendency for the amino group to donate electrons to the benzene pi-system and for the nitro group to accept them. The crest of a light wave passing through a molecule of para-nitroaniline may cause polarization of the molecule with the amino group donating charge and the nitro group accepting it. When the trough of the wave passes through, the influence may be to cause charge donation by the nitro group and acceptance by the amino group, which is against the nature of these structures. Thus, the response of the molecule is unsymmetrical; it is greater in one direction than the other. Para-nitroaniline is also transparent at many wave lengths of interest, including 0.532 .mu.m, which permits frequency doubling of the commonly used 1.064 .mu.m wavelength from a Nd:YAG laser. However, this molecule crystallizes in a centrosymmetric phase, and the second harmonic coefficients are, because of the synmetry conditions, zero.
Therefore, apart from the requirement for molecular hyperpolarizability, an organic molecule exhibiting second-order nonlinear optical effects must crystallize into a noncentric packing pattern, so that the second harmonic (.chi..sup.(2)) can be nonzero. A number of approaches have been taken to attain this result. The use of a chiral molecule ensures formation of a noncentrosymmetical crystal and mathematically guarantees a non-vanishing .chi..sup.(2), but not necessarily a large one. Another approach that is not understood, but that can work for biasing organic molecules to pack into noncentric structures, is to use polar aromatic molecules with meta-substitution patterns. For example, 2-methyl-4-nitro-aniline, as discloed by C. G. Bethea et al. in U.S. Pat. No. 4,199,698, has a nonlinear coefficient (d.sub.12) which is 5.8 times larger than the nonlinear coefficient (d.sub.31) of LiNbO.sub.3. It has also been reported that it is sometimes possible to obtain noncentrosymmetric crystals by cocrystallizing two similar compounds. For example, mixed crystals of para-nitroaniline and para-nitrophenol which exhibit SHG have been obtained by cocrystallization from solutions. See, Sov. J. Quantum Electron., 12, 214 (1982).
If a polarizable molecule which is transparent at the desirable wavelength packs in a noncentric crystal structure, then it will yield a useful nonlinear response when two additional criteria are met. First, the crystal must be phase matchable, in that there must be a propagation direction in the crystal where the incoming light and the second harmonic waves have coherent phases. Secondly, the molecular dipole moment vector should be aligned along or near to a particular direction of the crystal, with the exact direction being determined by the space group symmetry of the crystal. Since there is no method presently available to control either of these factors, the preparation of new organic crystals which exhibit nonlinear optical properties such as second harmonic generation remains a largely empirical art.
Therefore, although considerable progress has been made, both in understanding the electronic origins of molecular nonlinearities in organic .pi. systems, as well as in the hindsight explanation of the quantitative relationship of the molecular arrangements in a crystal to the observed nonlinearities, a need exists for new compounds having optimized nonlinear optical properties.